EECE502: Mathematical Methods in Engineering

 

Instructor: R. Sureshkumar, Professor, EECE, Washington University in Saint Louis.

 

Course Outline and Evaluation Policy

 

Guidelines for Term Project

 

Assignments

 

        “Warm up” Problems

  

                     HW1: Tensor Algebra

 

                     HW2: Matrices and Applications

 

                     HW3: Stability of Nonlinear Dynamical Systems

 

                     HW4: Linear ODEs, BVPs, Green’s function

 

                     HW5: Sturm-Liouville, Orthogonal Polynomials & Special Functions

 

                     HW6: Eigenfunction Expansion Technique for P.D.Es.

 

 

Some Topics for Discussion

 

Dimensional Analysis, Scaling, and Orders of Magnitude

Article by Astarita (Chemical Engineering Science, 52: 4681 (1997))

 

Visualization of Tensor Data

1.      Water diffusion in brain

2.      Heart muscle fiber reconstruction from MRI data

3.      Interactive deformations

4.      Hyperstreamlines

5.      Visualization of Coherent Structures in Turbulent Flows

(It is well-known that the dissolution of minute amounts of high MW polymers to turbulent flows can reduce the friction losses by up to 70%. Work by Kim, Adrian, Balachandar and Sureshkumar portray the effect of polymer additives on the dynamics of “hairpin” vortices, responsible for the production of turbulent (Reynolds) stress.)

1.      Effect of polymer additives on hairpin dynamics

2.      Newtonian flow hairpin dynamics  

3.      Low-moderate friction drag reduction

4.      High friction drag reduction

 

Elementary Stability Analysis: Applications beyond the CSTR

1.      Instability in Magma Flow (Science, 285: 1883 (1999))

2.      Modeling of Gene Networks (Bull. Math. Biol., 62: 247 (2000))

 

Pattern Formation

1.      Rayleigh-Benard Instability: Movie1, Movie2, Info, Benard-Marangoni Patterns

2.      Rayleigh-Taylor Instability: Movie1, Movie2, Movie3

3.      Kelvin-Helmholtz Instability: Movie1, Movie2

4.      Taylor-Couette Instability: Info, In polymer solutions (D.G. Thomas et al.): Spiral-to-ribbon

5.      BZ Reactions: Info, Analysis

6.      Turing Structures: Article

 

Useful Programs that Use LAPACK Subroutines Available from Netlib®

 

Nonlinear Algebraic Equations: Driver, Entire Code

 

Boundary Value Problem: Driver, Entire Code

 

Eigenvalue Problem: Driver, Entire Code

 

Commercial Software

 

Femlab®: Finite Element Solver with a Matlab® Interface. Available in the Chemical Engineering Learning Laboratory (CELL), Urbauer 218

 

Femlab® Primer (originally prepared by Arora and Sureshkumar for ChE366)

 

Fluent®: Finite Volume Method, Useful for Simulation of Fluid Flow.